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Paper Citation Record · LEDGER

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations

As of 8 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2508.18840.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2508.18840 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T16:23:06.616618Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

49 of 49 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5b950f86-c373-45e4-8355-5b21f34ec201 · outbound

This paper cites Alves, C.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Alves, C

Reference 1

Resolution
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Source-reported events for the cited work

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Observation 4b7c44c8-ac52-4b7e-a70c-cb42550e7388 · outbound

This paper cites Alves, C.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Alves, C

Reference 2

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation cd18ab5b-eb34-4d88-8a87-6d39f164998c · outbound

This paper cites Ambrosio, Concentration phenomena for a class of fractional Kirchhoff equations inRN with general nonlinearities.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Ambrosio, Concentration phenomena for a class of fractional Kirchhoff equations inRN with general nonlinearities

Reference 3

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation fee020dd-3a25-43d5-b042-9426b4358a99 · outbound

This paper cites Chang, R.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Chang, R

Reference 4

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation cafc0065-80ea-4439-a8d2-879c382325af · outbound

This paper cites Chang, V.D.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Chang, V.D

Reference 5

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 62de7d8d-b05b-4e19-8116-af09adfc8ba5 · outbound

This paper cites Cheng, S.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Cheng, S

Reference 6

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 5e6e5403-e077-45ea-9dad-371385edcf27 · outbound

This paper cites Di Nezza, G.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Di Nezza, G

Reference 7

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 6500f04e-002d-4abf-bda4-a84cbc26f1c5 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 8

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation f11a91e5-c960-40a2-9aee-d74ef2addbe7 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 9

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 69d0e3f5-bd6a-4839-a592-63ed7d425d62 · outbound

This paper cites Fiscella, E.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Fiscella, E

Reference 10

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation d9719ea4-a03d-4f93-8e6c-eedacaeffd9a · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 11

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation e182a6f5-1b02-473b-bde4-dda02eca4898 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 12

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 106679a4-aa10-4e8f-a6aa-4cf3912af7fe · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 13

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 7b80389e-57eb-4965-a610-4e955b7b7455 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 14

Resolution
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Observation 0a2dd8e3-db73-4de1-8b3c-c16051f0ec68 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 15

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 8cedc57c-edd0-402e-8559-228dc252581a · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 16

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation ff4568b4-93b3-4ee8-8df1-b6d932d00bde · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 17

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 23394679-e338-40dc-a931-9423720488e6 · outbound

This paper cites Huang, Y.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Huang, Y

Reference 18

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 8192ef56-4c44-4ab6-b5a1-23eed9bc8d0f · outbound

This paper cites Isernia, Sign-changing solutions for a fractional Kirchhoff equation.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Isernia, Sign-changing solutions for a fractional Kirchhoff equation

Reference 19

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation d0e4c49e-bea0-4efe-8d43-66369f832170 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 20

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 3f1bcae8-e0be-4e04-97b3-21246f1bd13f · outbound

This paper cites Laskin, Fractional quantum mechanics and L´ evy path integrals.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Laskin, Fractional quantum mechanics and L´ evy path integrals

Reference 21

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 342ec525-5ca9-44f2-93aa-010c9b4e6509 · outbound

This paper cites Lei, Multiple positive solutions for a fractional Kirchhoff type equation with logarithmic and singular nonlinearities.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Lei, Multiple positive solutions for a fractional Kirchhoff type equation with logarithmic and singular nonlinearities

Reference 22

Resolution
verified fuzzy
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 1a4ef456-1a53-4922-8fb4-9dba44808c18 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 23

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 8f29350d-a171-4ebf-aaec-c394b3e2a70b · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 24

Resolution
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 2c5e09a2-f7bf-4cec-86e3-55886b82cbe1 · outbound

This paper cites L¨ u, Ground states of a Kirchhoff equation with the potential on the lattice graphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations L¨ u, Ground states of a Kirchhoff equation with the potential on the lattice graphs

Reference 25

Resolution
verified fuzzy
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation cfd19060-fd08-40b3-ad02-8fb8fc883d4b · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 26

Resolution
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raw_fallback, observed 2026-08-05T16:23:07.054426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation ef293b1d-4f42-4b93-bf0f-fb66f7e620d0 · outbound

This paper cites Ouaziz, Abdesslam and A.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Ouaziz, Abdesslam and A

Reference 27

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation bf57cd97-b705-41bd-b12b-9588609695c1 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 28

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 2df6f2ae-1ab0-4377-aa8b-d0db4a8f2f50 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:07.001658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 97608607-6f60-4daf-a562-a79bfbde24d3 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.986766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 847eb1e6-2433-41e6-ab40-c0406d04e9e7 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.971861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 32ac1ca8-5659-43a2-a60e-2dfbf651c51b · outbound

This paper cites Shuai, Existence and multiplicity of solutions for logarithmic Schr¨ odinger equations with potential.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Shuai, Existence and multiplicity of solutions for logarithmic Schr¨ odinger equations with potential

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.956707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 5794648c-7d68-4784-bb2d-bc4a0dfef29f · outbound

This paper cites Wang, Solutions to discrete nonlinear Kirchhoff-Choquard equations.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, Solutions to discrete nonlinear Kirchhoff-Choquard equations

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.941518Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation f01165d8-b248-4ada-bde9-897f311f64e8 · outbound

This paper cites Wang, Solutions to discrete fractional Schr¨ odinger equations.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, Solutions to discrete fractional Schr¨ odinger equations

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.925644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation bc689855-7424-4fdf-8c94-0e329ffb2e76 · outbound

This paper cites Wang, A class of p-Laplacian equations on lattice graphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, A class of p-Laplacian equations on lattice graphs

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.909625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.546875Z digest=sha256:7f3beb92f882b3963aaaa1bd0a5bb51168daf32ea6119a15da531a4a9df89b15

Observation 1c415c6a-dbeb-410b-8419-e3ad6f0e68e1 · outbound

This paper cites Wang, Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, Solutions to discrete nonlinear Kirchhoff-Choquard equations with power nonlinearity

Reference 36

Resolution
verified exact
doi, observed 2026-08-05T16:23:06.657060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 3cd5a2f0-03d8-4eed-8e66-98f0b4f02c3e · outbound

This paper cites Fractional logarithmic Schr\"{o}dinger equations on lattice graphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Fractional logarithmic Schr\"{o}dinger equations on lattice graphs

Reference 37

Resolution
verified exact
local_arxiv, observed 2026-08-05T16:23:06.729013Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation bd70fbd6-26b9-46f9-93d6-8ff99532ed55 · outbound

This paper cites Wang, Sign-changing solutions to discrete nonlinear logarithmic Kirchhoff equations.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wang, Sign-changing solutions to discrete nonlinear logarithmic Kirchhoff equations

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.892897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.563390Z digest=sha256:62fe7793ab78977185d94d48b0be2a27955d814f727c227fe88eb8d2a0ac368e

Observation 35ba20f3-fb86-4051-9721-e2b93e3a2edc · outbound

This paper cites Eigenvalue estimates for the fractional Laplacian on lattice subgraphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Eigenvalue estimates for the fractional Laplacian on lattice subgraphs

Reference 39

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unresolved
no resolver link, observed 2026-08-05T16:23:06.568627Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation ca70113b-7b82-45e3-bcdd-c4354bdf5446 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.877114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.573512Z digest=sha256:873dac96aeba185e2f81ff8a571832a0c4a917abec8a2ea811a13db2223c5e48

Observation 368f19ec-f01d-4268-8448-8c617f346092 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.860778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.577890Z digest=sha256:ba89477c2f441cb123649015539afc2cdcb3083e01b7d0fa5f242de7bfffae07

Observation d94fb814-47c6-4291-b7bc-86c0cfb1254f · outbound

This paper cites Wu, Infinitely many positive multi-bump solutions for fractional Kirchhoff equations.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Wu, Infinitely many positive multi-bump solutions for fractional Kirchhoff equations

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.845995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.582954Z digest=sha256:26534a7c41deca96f577cc961111dcbbdb77c03c52c021ab3c7acd8af1d9cfcf

Observation 0895bea5-a74f-4ada-8db5-9831c6ff6943 · outbound

This paper cites Xiang, D.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Xiang, D

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.829816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.587458Z digest=sha256:c942268ce1de99f56fc5cc25175a940b902c71cca19a6581d48978ed77b74aa7

Observation a6d27eb4-a267-488b-b081-a5acec587f6f · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.813919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.591816Z digest=sha256:cd772fe5351dc276de3fa60f39f77cedfe9108daeb276d55128c1b851ee2594d

Observation 4438a391-89c9-4142-afed-1dd765df2833 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.797984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.596920Z digest=sha256:79b60feac74c17682a70864efef02166148e5c7e30341e47a788364f09b7e204

Observation 0225fda5-f791-472a-8f88-a9f479342147 · outbound

This paper cites an unresolved cited work.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-05T16:23:06.781316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.601806Z digest=sha256:3c72cd27fe0bd1dbdf2663c357d8d53381b8edf00dbbaca15a0e7fc8504b9b9f

Observation 00abcedb-ebb0-478c-8e97-0a7a8cb10b99 · outbound

This paper cites Zhang, X.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Zhang, X

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.765447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.606501Z digest=sha256:853f92ca185076caa73ee2487524aa9d0e109ebbf7d18b1bde454cb3bd6c9c1f

Observation a32a24fa-5f52-45e2-931b-8c501f6d6214 · outbound

This paper cites Fractional Laplace operator and related Schr\"odinger equations on locally finite graphs.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Fractional Laplace operator and related Schr\"odinger equations on locally finite graphs

Reference 48

Resolution
verified exact
local_arxiv, observed 2026-08-05T16:23:06.682025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.611389Z digest=sha256:a8295841ab38d63c7bdf3f46dad991eccea54dd3c91705adff53d18697df98ed

Observation 038d6901-388a-411e-bad1-2726af87c213 · outbound

This paper cites Zloshchastiev, Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational con- sequences.

Existence and multiplicity of solutions to discrete fractional logarithmic Kirchhoff equations Zloshchastiev, Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational con- sequences

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T16:23:06.748373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-05T16:23:06.616618Z digest=sha256:90a8b9daf6506ef47b2e15448264e91818cde2f6668fc8f19b08cfdc4cd98c5d

Pith citing papers

No inbound Pith citation observations are available.